These beings believe that Martin intends to have Arya end up killing several important someones. Not sure which ones, but at least one of the candidates for the iron throne is on the list, probably several.

It is an easy way to pass across the sea, yet not the only one available to the faceless. Sailors at home in that city will probably let someone pass on their ships across the sea free of charge provided that they know he/she serves the many-faced god. Further training by the faceless is pretty much guaranteed. A single kill here or there is nothing compared to what one of the faceless needs to know. There are, however several others that could recognize her besides Jon. Brandon stark, Rickon Stark, and Howland Reed. The last one is pretty much guaranteed to live for a while yet, as he is the only one that knows the truth about the vow Lyanna stark got Ned to swear, possibly the truth about Jon Snow being half Stark, half Targaryen. When her training is done with the faceless, the question is not who might recognize her, but instead who will be allowed to do so. She might not be wearing her own face much of the time.